1. Field of the Invention
The present invention relates to a power system control apparatus for controlling a power system and, more particularly, to a power system control apparatus having an auto voltage regulator (to be referred to as an AVR hereinafter) and a power system stabilizer (to be referred to as a PSS hereinafter) connected to the AVR.
When the state of a power system is changed due to a variation in load, connection/disconnection of the system, or the like, the generator terminal voltage is changed to cause a power fluctuation.
In this case, an AVR for controlling the excitation voltage is used as a power system control apparatus for stabilizing the generator terminal voltage. With only the AVR, however, the power fluctuation caused by the variation in load cannot be sufficiently suppressed.
For this reason, a PSS has been put into practical use together with the AVR since the late 1960s to stabilize the power system. The PSS is a unit for increasing an effect for suppressing the power fluctuation by excitation control of a power generator.
It is a known fact that stability of a power system is greatly changed by a power system impedance and a phase difference angle between a generator terminal voltage and an infinite bus voltage. In order to maintain the power system stable under any operating condition, it is preferable to change control gains of the AVR and the PSS in accordance with a state of the power system, particularly the power system impedance and the phase difference angle. Conventionally, in order to change the control gain, the power system impedance is estimated, thereby adjusting the control gain of the PSS.
For example, in a model of a power system (single-generator-coupled infinite bus system) 5 as shown in FIG. 1, in which an infinite bus 1 is coupled to a single generator 3, the amplitude and phase of its voltage eb are constant. An effective (active) power Pe and a reactive power Q can be expressed as follows: EQU Pe=(eq+Xq.multidot.id).vertline.et.vertline..multidot.sin.perspectiveto./(X e+Xq) (1) EQU Q=(eq+Xq.multidot.id) id-Xq.multidot.i.sup.2 (2)
where
e.sub.q : internal quadrature-axis reactance voltage PA1 id: load current of direct axis PA1 Xq: quadrature-axis synchronous reactance PA1 .delta.: phase difference angle PA1 i: load current PA1 .omega..sub.0 : alternate frequency PA1 Tm: mechanical torque PA1 Te: electrical torque PA1 D: intrinsic braking torque coefficient (braking coefficient) PA1 Xd': direct-axis transient reactance PA1 Xd": direct-axis initial transient reactance PA1 Tdo": open-circuit initial time constant PA1 Xq: quadrature-axis synchronous reactance PA1 Xq": quadrature-axis initial transient reactance PA1 Tqo": short-circuit initial time constant
Note that the generator terminal voltage e.sub.t can be expressed by the following equation and assume that Xq=0. EQU et.sup.2 =eq.sup.2 +ed.sup.2 (3)
The active power Pe and the reactive voltage Q can be transformed as follows: EQU Pe=et.multidot.eb/Xe.multidot.sin.delta. (4) EQU Q=et.sup.2 /Xe-et.multidot.eb/Xe.multidot.cos.delta. (5)
where e.sub.d is the internal synchronous reactance voltage (=Xq.multidot.id).
When the voltage e.sub.b of the infinite bus which is difficult to measure is cancelled from equations (4) and (5), the phase difference angle .delta. can be obtained from the following equation including amounts (the generator terminal voltage e.sub.t, the active power Pe, and the reactive voltage Q) that can be easily measured and Xe: EQU .delta.=arctan{Pe/(et.sup.2 /Xe-Q)} (6)
Conventionally, when several presumed Xe values are to be obtained, the corresponding active power Pe, reactive power Q, and generator terminal voltage e.sub.t are substituted in equation (6) to obtain phase difference angles .delta..sub.1, .delta..sub.2, . . . , and .delta..sub.n.
These calculated different phase difference angles .delta. are compared with corresponding internal phase difference angles .delta..sub.gen measured at the generator terminal. An Xe value that yields a phase difference angle .delta..sub.i providing the minimum change over time is determined as the power system impedance at this time.
A conventional unit for estimating the power system impedance Xe comprises parameter measuring devices 9a to 9d, phase difference angle arithmetic units 11a to 11c, difference circuits 13a to 13c, correlation arithmetic units 15a to 15d, and a comparator 17, as shown in FIG. 2. According to the conventional impedance estimating unit, the comparison between a phase difference angle .delta..sub.i (1.ltoreq.i.ltoreq.n) and an internal phase difference angle .delta..sub.gen is performed by obtaining their correlation. An Xe value that yields the maximum correlation is estimated as the power system impedance Xe.
With this conventional method, the phase difference angle .delta. is obtained by equation (6) to estimate the power system impedance Xe under an assumption that Xq=0. In practice, however, the quadrature-axis synchronous reactance Xq is as large as 1.5 pu (per unit) whereas the power system impedance Xe is as small as about 0.4 pu. Hence, equation (6) includes a significant error.
In the conventional method, the power system impedance Xe is estimated by obtaining the correlation between change in phase difference angle .delta., calculated in accordance with above equation, and that in internal phase difference angle .delta..sub.gen. Hence, the estimated power system impedance Xe includes a significant error.
Furthermore, when several different power system impedances Xe are to be estimated in a real time manner, a plurality of phase difference angles .delta. are calculated by equation (6), and the correlation between the phase difference angle .delta. and the internal phase difference angle .delta..sub.gen is obtained. Therefore, a large amount of calculation is needed, and many power system impedances Xe cannot be estimated from equation (6) in a real time manner. For this reason, in practice, about three different power system impedances Xe are estimated. As a result, the estimated power system impedance Xe is not very accurate.
Since the correlation between the phase difference angle .delta. and the internal phase difference angle .delta..sub.gen is obtained as a function of time, the power system impedance Xe can only be estimated when a certain period of time elapses after the correlation is obtained. As a result, it is impossible to instantaneously estimate an abrupt change in power system impedance Xe to suppress fluctuation in the power system upon system disconnection and the like.
The power system stabilizer PSS for suppressing the fluctuation of the system is to be described with reference to FIG. 3.
FIG. 3 shows a typical example of a conventional power system control apparatus 19. The power system control apparatus 19 comprises an AVR 21 and a PSS 23. Excitation is performed only by a thyristor.
The basic operation of the AVR 21 is to control the excitation voltage by using the thyristor such that a difference between a terminal voltage e.sub.t, measured by passing through a noise eliminating filter 25a, and a target voltage value e.sub.tref is reduced. An actual AVR 21 also includes a damping circuit and the like. In FIG. 3, the damping circuit is indicated as a gain/leading-delaying circuit 27.
At this time, the PSS 23 corrects the target voltage value e.sub.tref to indirectly control the excitation voltage.
As shown in FIG. 3, the PSS 23 generally has a reset circuit 29, a phase compensating circuit 31, a limiter 33a, and a noise eliminating filter 25b. FIG. 4 shows the response of the active voltage Pe when the target voltage value e.sub.tref is changed in a stepwise manner to control the cross-compound type thermal power generator having a rated power of 600 MW by using the PSS 23.
As is apparent from FIG. 4, when only the AVR 21 is used, fluctuations of 12.6 MW and 7.1 MW, at the first and second peaks, respectively, are excited. In contrast to this, when the PSS 23 is coupled to the AVR 21, the fluctuation of 7.4 MW at the first peak is converged.
In this manner, the PSS 23 has a good performance for suppressing a fluctuation in power system near the rated point.
The PSS 23 is a linear control circuit, as described above. In contrast to this, however, the power system does not have linear characteristics at all. These characteristics will be explained by way of the infinite bus system 5 coupled to a single generator as shown in FIG. 1.
In the infinite bus system 5 shown in FIG. 1, the dynamic characteristic of the phase difference angle .delta. that governs the power and voltage at the generator terminal is expressed by the following equation: ##EQU1## where M: unit inertia constant.times.2
The braking characteristic based on the phase difference angle .delta. is determined by the intrinsic braking torque coefficient D. When the coefficient D is large, the phase difference angle .delta. becomes stable against the disturbance, whereas when it is small, the angle .delta. fluctuates. When the angle .delta. fluctuates, the active power Pe fluctuates accordingly. The intrinsic braking torque coefficient D largely depends on the power system impedance Xe and the phase difference angle .delta.. ##EQU2## where e.sub.b : infinite bus voltage
FIG. 5 shows the characteristics of the braking coefficient D associated with the parameter (power system impedance) Xe and the phase difference angle .delta., both of which change during operation of the generator.
The larger the power system impedance Xe and the closer the phase difference angle .delta. to 90.degree., the smaller the braking coefficient D. Namely, the phase difference angle and the power system impedance of the single-generator-coupled infinite bus system 5 vary.
FIGS. 6A and 6B show the response state of the single-generator-coupled infinite bus system 5 when the power system impedance Xe is changed in a stepwise manner. When the power system impedance Xe is changed from 0.2 pu to 0.3 pu, both voltage and power are well controlled by the effect of the PSS 23. Namely, the fluctuation in voltage and power is suppressed within a short period of time.
When the power system impedance Xe is changed from 0.2 pu to 1.0 pu, the conventional PSS 23 does not have a sufficiently large braking force and it takes considerable time to suppress the fluctuation in power. This is because in the conventional PSS 23 the power system impedance Xe becomes large and the phase difference angle .delta. becomes 70.degree. or more, and thus the braking coefficient D becomes small.
In this manner, in the conventional PSS 23, when the power system impedance is changed largely due to partial disconnection of the power system, or the like, the braking characteristic is degraded
When the power system impedance is largely changed due to a fluctuation in load, the braking characteristic of the PSS against the fluctuation in power is degraded.